Answer:
Heights of 29.5 and below could be a problem.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean 
and standard deviation 
, the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The heights of 2-year-old children are normally distributed with a mean of 32 inches and a standard deviation of 1.5 inches.
This means that 
There may be a problem when a child is in the top or bottom 5% of heights. Determine the heights of 2-year-old children that could be a problem.
Heights at the 5th percentile and below. The 5th percentile is X when Z has a p-value of 0.05, so X when Z = -1.645. Thus
Heights of 29.5 and below could be a problem.
Answer:
Line PU has points R and S between points P and U, lines QR and ST are parallel, line QR intersects line PU at point R, line ST. intersects line PU at point S, the measure of angle PRQ is 135 degrees, and the measure of angle UST is 15 ( x plus 2 ) degrees. X = −1 x = 7 x = 9 x = 13
Step-by-step explanation:
Answer:
14.04°
Step-by-step explanation:
In this right triangle, we're seeking the measurement of an angle at the base of the triangle and we have the measurements of two of the sides (none are the hypotenuse) : the opposite one of the angle and the adjacent side.
The relationship between the two sides we have the measurement and the angle we are looking for is the tangent:
To find the angle we do an arctan on 0.25 and we get an angle of 14.04 degrees.
Answer:
f(x) - 3 is translated 3 units down and -2*f(x) is reflected across x-axis.
Step-by-step explanation:
We have, f(x) becomes f(x) - 3.
The y-intercept of f(x) is f(0), this implies y-intercept of f(x) -3 is f(0) - 3. This means that the graph of f(x) is translated 3 units down.
Next, we have f(x) becomes -2*f(x).
The y-intercept of -2*f(x) is -2*f(0) and it means that first the graph of f(x) is stretched horizontally by 2 units and then reflected across x-axis.
As, the function f(x) is multiplied by 2, this implies that resultant function -2*f(x) will be an even function and its graph will be symmetric about y-axis.
Moreover, the function -2*f(x) increases wherever f(x) decreases and vice-versa.
